How to get the beginning position of each line of a text object (Pyhton)
The bounding box

Many of the kerning options for the text object are available. IIRC there is another answer (unfindable so far) that uses these to calculate the  positions.
Instead I'm going to simply use the bounding box, single first line, 2 lines, 3 lines etc.
The bounding box is the local axis aligned extent of an object, in local coordinates.  The box has 8 coordinates, the zeroth coordinate is the front bottom left hand corner. eg (-1, -1, -1) for default cube  Multiplying by objects matrix world gives the global location.
Test script adds an empty at beginning of each line of the text object that has context.
Answer for version 2.8.  For 2.7x would use a scene.update() to rejig for changes to text body.
import bpy
from mathutils import Vector

context = bpy.context
dg = context.evaluated_depsgraph_get()
ob = context.object
mw = ob.matrix_world
text = ob.data.body

lines = text.split(&quot;\n&quot;)
for i, l in enumerate(lines):
    ob.data.body = &quot;\n&quot;.join(lines[:i + 1])
    dg.update()
    bbox = [Vector(b) for b in ob.bound_box]
    bpy.ops.object.empty_add(
            location=mw @ bbox[0]
            )

Related Counting amount of lines in a text object